Erratum: Quantum mechanics of a constrained electrically charged particle in the presence of electric currents [Phys. Rev. A80, 052109 (2009)]

Abstract

Erratum: Quantum mechanics of a constrained electrically charged particle in the presence of electric currents [Phys. Rev. A 80, 052109 (2009)]

Quantum Mechanics on Surfaces

“…This will induce spin-orbit couplings which will add motion dependent potentials. The effect of these can be very pronounced (26). Clearly, much more work needs to be done in this field, but it is work which apparently has potential to further advance recent discoveries in physics.…”

“…These new coordinates should therefore be well suited to explore the physical states of a quantum particle on the catenoid. Let us now consider the Schrödinger equation (26). In terms of the new coordinates we have in particular that…”

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

“…In a general form, the previously discussed system can be described by a canonical action integral [13,14,18] as…”

“…Under certain conditions, for the electromagnetic field a proper gauge should be chosen [13]. At the same time, the presence of the electromagnetic field determines that the motion equation of the vector potential for the electromagnetic field should be included [14]. However, there is no an explicit fundamental framework of the JKC procedure to study the quantum equation, the chosen gauge and the motion of the vector potential simultaneously.…”

“…The absence may lead to some calculational ambiguities [15]. Generally, the curved system in an electromagnetic field can be described by a canonical action integral [14,18]. By performing partial integration, the action can be divided into a volume integral and a surface integral.…”